The jocular noun rumpy-pumpy denotes sexual intercourse.
—Hence the phrase a bit of rumpy-pumpy, which designates:
– a (prospective) sexual partner;
– a sexual encounter.

The noun rumpy-pumpy occurs, for example, in the review of Hamnet, Lolita Chakrabarti’s adaptation of Maggie O’Farrell’s 2020 novel, produced at the Swan Theatre, Stratford-upon-Avon—review by Susannah Clapp, published in The Observer (London, England) of Sunday 16^th April 2023:

Wittily billed as “William, Agnes’s husband”, Tom Varey makes Shakespeare a convincing scruff, as eager for rumpy-pumpy among ripening fruit as for stage success.

The noun rumpy-pumpy is a reduplication (with variation of the initial consonant and addition of the suffix -y) of the noun rump, denoting a person’s buttocks.
—Likewise, the noun ass, denoting a person’s buttocks, is used to designate sexual intercourse and a person considered as a source of sexual satisfaction.

The earliest occurrences of the noun rumpy-pumpy that I have found are as follows, in chronological order:

1-: From The Scottish National Dictionary (entry first published in 1968; revised in 2005):

RUMP, n., v. Sc. usages:
I. n. 1. In phr. and derivs.: (1) rump and stump, completely, wholly, in its entirety, to the very last piece or fragment (Ayr.4 1928; Ork., em. and wm.Sc., Wgt., Uls. 1968) […]; (2) rumpie, rumpy, (i) a small crusty loaf or roll (Per., Dmb., Gsw. 1968); (ii) comb. rumpy-bum, of a coat; tailless, cut short; (iii) comb. rumpie-pumpie, a jocular term for copulation (Ayr. 1968); †(3) rumpock, dim., used as a nickname for a person whose queue of hair has been cut short.

2-: From the review of Go Slowly, Come Back Quickly, a novel by the British actor and author David Niven (1909-1983)—review by Ron Robinson, published in The Winnipeg Sun (Winnipeg, Manitoba, Canada) of Sunday 31^st October 1982:

Compared with most best-sellers’ graphic portrayal of men and women engaged in rumpy-pumpy, this book is chaste.
There’s even (blush!) romance. Boy meets girl, boy loses girl, they pause for a misunderstanding, then the couple gets what they deserve.

3-: From Born to be King, an episode of the British television comedy series Blackadder, written by Richard Curtis (born 1956) and Rowan Atkinson (born 1955), first broadcast on BBC One on Wednesday 22^nd June 1983:

McAngus: You must be the king’s wee bit of rumpy-pumpy.
Queen: I am the queen.

4-: From the review of The ABC’s of STD, by Alan Meltzer—review by Ron Robinson, published in The Winnipeg Sun (Winnipeg, Manitoba, Canada) of Sunday 2^nd October 1983:

This book is not for Old Testament types who want wrongdoers corrected by bolts of moral lightning and claps of thunder. In his only moral statement on STD’s, Meltzer suggests that STD can also mean stay tenderly devoted. Staying with one partner is a practical means of limiting the spread of these diseases.
Reading his book is another. The descriptions of symptoms and long term effects are enough to put you off rumpy-pumpy for a month.

5-: From At the cinema—with Roy Martin, published in the Evening Post (Reading, Berkshire, England) of Thursday 16^th October 1986:

I would dearly like to tell you about another new film called Oxford Blues (15 certificate, ABC Reading from tomorrow). But this is another movie which the distributors have coyly slipped out without any advance information.
You can expect some mild rumpy-pumpy as it stars Rob Lowe and Ally Sheedy, two handsome members of the so-called Hollywood ‘brat pack’.
Despite its title, it doesn’t necessarily have much to do with the University city.

6-: From The Music Scene with Chris Eary, published in the Evening Post (Reading, Berkshire, England) of Saturday 8^th November 1986:

Millie Jackson—An Imitation Of Love (Jive): Shy, retiring Ms Jackson is best known for her preoccupation with what is widely known as rumpy-pumpy, and while this LP isn’t as graphic as some, it is [sic] still maintains a raunch factor.

A synonym of rumpy-pumpy, rumpo is from the noun rump and the suffix -o, used to form slang and colloquial nouns, adjectives and interjections.
—Cf. also blotto.

The earliest occurrence of the noun rumpo that I have found is from the column Keith Waterhouse on Monday, by the British author and newspaper columnist Keith Waterhouse (1929-2009), published in the Daily Mirror (London, England) of Monday 18^th March 1974:

There is bound to be a storm over the controversial new film “The Publicist” which opens at sixty-five West End cinemas this week.
[…]
Mrs. Mary Press-Cuttings is expected to add her two-pennorth shortly. If, as is confidently expected, she calls for a ban on “The Publicist” on the grounds that it is lewd, distasteful, and contains explicit scenes depicting a teenager having rumpo with a nun, overflow screenings will be organised at Wembley Stadium, Earls Court and Olympia.